Adrian is painting the outside of a cylinder that he plans to

Question

use as a coffee table. The cylinder has a radius of 4 feet
and a height of 3 feet.
Adrian wants to paint all around the outside of the cylinder,
including the top and bottom faces.
In order to understand how much paint is needed, he wants
to know the surface area of the outside of the cylinder. What
is the surface area of the cylinder, rounded to two decimal
places?
*Hint: Don't forget to use your Desmos calculator and STAAR
Reference Sheet to help!
Remember to use the symbol on your Desmos calculator.

Answer 1

To find the surface area of a cylinder, you need to calculate the surface area of the curved part plus the area of the top and bottom circular faces.

The formula for the surface area \( A \) of a cylinder is given by:

\[ A = 2\pi rh + 2\pi r^2 \]

Where:

• \( r \) is the radius of the cylinder,
• \( h \) is the height of the cylinder,
• \( \pi \) is approximately 3.14159.

For this problem:

• The radius \( r = 4 \) feet
• The height \( h = 3 \) feet

Now, we can substitute these values into the formula:

1. Calculate the lateral surface area (curved part): \[ 2\pi rh = 2\pi(4)(3) = 24\pi \]

2. Calculate the area of the top and bottom circular faces: \[ 2\pi r^2 = 2\pi(4^2) = 2\pi(16) = 32\pi \]

3. Now add both areas to get the total surface area: \[ A = 24\pi + 32\pi = 56\pi \]

Now, using \( \pi \approx 3.14159 \): \[ A \approx 56 \times 3.14159 \approx 175.929 \]

Finally, rounding to two decimal places: \[ A \approx 175.93 , \text{square feet} \]

So, the surface area of the cylinder, rounded to two decimal places, is 175.93 square feet.